Binary half tone photomasks and microscopic three-dimensional devices and method of fabricating the same

ABSTRACT

The present invention generally relates to improved binary half tone (“BHT”) photomasks and microscopic three-dimensional structures (e.g., MEMS, micro-optics, photonics, micro-structures and other three-dimensional, microscopic devices) made from such BHT photomasks. More particularly, the present invention provides a method for designing a BHT photomask layout, transferring the layout to a BHT photomask and fabricating three-dimensional microscopic structures using the BHT photomask designed by the method of the present invention. In this regard, the method of designing a BHT photomask layout comprises the steps of generating at least two pixels, dividing each of the pixels into sub-pixels having a variable length in a first axis and fixed length in a second axis, and arraying the pixels to form a pattern for transmitting light through the pixels so as to form a continuous tone, aerial light image. The sub-pixels&#39; area should be smaller than the minimum resolution of an optical system of an exposure tool with which the binary half tone photomask is intended to be used. By using this method, it is possible to design a BHT photomask to have continuous gray levels such that the change in light intensity between each gray level is both finite and linear. As a result, when this BHT photomask is used to make a three-dimensional microscopic structure, it is possible to produce a smoother and more linear profile on the object being made.

FIELD OF THE INVENTION

[0001] The present invention generally relates to binary half tone(“BHT”) photomasks and three-dimensional microscopic structures (e.g.,micro-electromechanical systems (“MEMS”), micro-optics, photonics,micro-structures, imprint lithography applications and other devices)and a method for designing and fabricating the same.

BACKGROUND OF THE INVENTION

[0002] Recent technological advances have made it possible to usethree-dimensional MEMS, micro-optical devices and other micro-structuresin a variety of fields, including photonics, communications, andintegrated circuits. In the past, these tiny devices were fabricatedusing laser micro-machining tools. However, this method was timeconsuming and expensive, and thus, it was typically difficult formanufacturers to meet production requirements in a cost efficientmanner. In this regard, such techniques did not work well with commonlyapplied techniques for manufacturing integrated circuits because eachpixel of the design had to be rewritten using a new algorithm. Sincethis was a laborious and time-consuming undertaking, many have avoidedthe use of micro-machining tools.

[0003] In light of the desirability to use small scale,three-dimensional structures, other manufacturing techniques have beendeveloped in an attempt to avoid the problems associated with lasermicro-machining tools. In particular, traditional optical lithographytechniques used for fabricating integrated circuits have been adapted tomanufacture three-dimensional microstructures. In traditional opticallithography, a fully resolved pattern is etched into a binary photomaskand transferred to a wafer by exposing the wafer through an exposuretool (e.g., stepper). More particularly, binary photomasks are typicallycomprised of a substantially transparent substrate (e.g., quartz) and anopaque layer (e.g., chrome) in which the pattern to be transferred isetched. It is also known that other layers may be included on thephotomask, including, for example, an antireflective layer (e.g., chromeoxide). The photoresist in the substrate on the integrated circuit beingprocessed is then developed and either the exposed or unexposed portionsare removed. Thereafter, the material on the substrate is etched in theareas where the photoresist is removed. An example of the technologyinvolved in manufacturing a traditional binary photomask (e.g.,chrome-on-quartz) and its use to manufacture integrated circuits isdisclosed in, for example, U.S. Pat. No. 6,406,818.

[0004] These known processes for fabricating binary photomasks andsemiconductor devices have been modified for the manufacture ofthree-dimensional, microscopic devices. In this regard, it is known touse a continuous tone pattern on the photomask (e.g., chrome-on-glass)instead of a binary, fully resolved mask pattern to yield a continuoustone intensity through the photomask during image formation. One type ofcontinuous tone, variable transmission photomask is commonly known as abinary half tone (“BHT”) photomask. BHT photomasks use two levels ofgray tones (e.g., 0% transmissive and 100% transmissive). Another typeof continuous tone, variable transmission photomask is known as grayscale photomasks, which use varying levels of transmission of lightthrough the photomask (e.g., 0%, 50%, 100%, etc.). By using these typesof variable transmission photomasks, a three-dimensional structure canbe formed in the photoresist on a wafer through the use of a continuoustone pattern.

[0005] BHT photomasks are typically designed to have sub-resolutionfeatures that partially transmit exposure source light intensity basedon feature modulation in width and pitch. In this regard, it is known inthe art to design a BHT photomask layout for microscopic surfaces bydividing the patterned area of the photomask into pixels and sub-pixels(commonly referred to as “sub-pixelation”) which define areas on themask through which light is to be transmitted, as shown in FIGS. 1 and2. The sub-pixels defining the BHT photomask pattern are designed to besmaller than the resolution of the exposure tool being used so that agray scale image can be created on the resulting wafer. The boundariesof the sub-pixel's size are typically defined by Rayleigh's equation (1)as follows:

R=kλ/NA  (1)

[0006] where R is the minimum resolvable half pitch feature of thewafer, λ is the exposure tool wavelength, NA is the numerical apertureof the optical system of the exposure tool being used and k (k factor)is a unitless constant whose value depends on process capability (e.g.,the smaller the k factor, the better low contrast aerial images can beseen). Generally speaking, the sub-pixels that are required by grayscale designs need to be unresolved in the imaging system, and thus, thek factor should preferably be less than 0.5. As a practical matter,however, the k factor can be somewhat greater than 0.5 and still beunresolved by the total process for some exposure tools. Photomaskdesigners have used calibrated simulation tools, such as the Prolith/2manufactured by KLA-Tencor, to converge on the optimum unresolvablefeature size. Unfortunately, there are many other tools which do notmeet the requirements of equation (1), and thus, the design of thephotomask is often limited by the capabilities of the design toolsavailable to the designer. Moreover, since photomasks are commonlydesigned to include other structures (e.g., two dimensional, binarycomponents such as integrated circuit patterns) in addition to athree-dimensional device (e.g., photonics application), this problem iseven more complex than implied by the above equation. In such cases,certain BHT cell designs may involve isolated spaces in chrome or chromeislands on the mask and the notion of half pitch is not defined.

[0007] As understood by those skilled in the art, tolerable surfaceroughness effects the minimum feature size in the device underfabrication. For example, where the k factor is 0.7 in equation (1)(i.e., the minimum feature size is resolvable by the optical system), anattempt to construct a BHT photomask having a step-ramp layout willresult in a sub-ripple within each step of the ramp pattern, as shown inFIG. 3. In some applications where the specifications of the devicepermit, a ripple-effect may be acceptable, albeit undesirable. However,in many applications, a sub-ripple effect is not acceptable since asmoother profile is needed for optimal performance of the device beingfabricated. Since the prior art BHT photomask design requires the use ofa small k factor to achieve a smoother profile, the mask designer islimited to equipment meeting this requirement.

[0008] In addition to the k factor, the design of a BHT photomask layoutis governed by other specifications of the optical lithography equipmentbeing used, including, for example, its resolution, magnification,wavelength, etc. In this regard, known gray scale applications, such asmicro-optical surface generation, require data to have a higherresolution than what is typical of most mask pattern generators. As aresult, the mask designer is limited to only those write tools that havethe ability to match the gray level grid design associated therewith.For example, an electron beam write tool such as the MEBES 4500, with awrite grid of 20 nm cannot properly replicate a BHT design whosesub-pixel variations is 10 nm. A laser beam write tool, by contrast,such as the ALTA 3500 having a write address of 5 nm is capable ofreplicating the same design.

[0009] Moreover, an imaging solution requiring custom materials at themask will often add cost and complexity in the overall manufacturingprocess due to the difficulties typically associated with integratingnew materials into a photomask. For example, it is known in the art touse variable attenuating films (“VAF”), rather than a BHT photomask, tomake three-dimensional devices. However, VAFs are typically expensiveand yield less than desirable results.

[0010] Once the mask pattern design is completed, the design istransferred to the photomask using optical lithography methods similarto those used to process a conventional binary photomask, as shown inFIG. 4. More particularly, a binary photomask having photoresist 51,chrome 53 and quartz 55 layers is placed under a photomask patterngenerator. The photoresist layer 51 is exposed to an optical, laser,electron beam or other write tool in accordance with the data filedefining the BHT photomask. The exposed portions of the photoresistlayer 51 are developed (i.e., removed) to expose the underlying chromeportions of the chrome layer 53. Next, the exposed chrome portions areetched away (e.g., by dry plasma or wet etching techniques). Thereafter,the remaining photoresist 51 is removed to form a completed BHTphotomask in accordance with the BHT photomask layout.

[0011] The variable intensity gray tone pattern defined by the mask isnext transferred to a wafer coated with photoresist using a waferstepper or other optical lithography tools. More specifically, varyinglight intensities are exposed to portions of photoresist on the wafer asdefined by the openings in the BHT photomask. The photoresist, in turn,exhibits changes in optical density and a gray scale profile is createdthereon. It is noted, however, that the photoresist process is oftenlimited to the variable dose pattern generator being used. Next, theexposed photoresist is removed and the remaining photoresist forms agray scale pattern which corresponds to the mask design. The photoresistand wafer are then etched to predetermined depths to conform to the grayscale pattern. The result is a three-dimensional micro-structure on thewafer.

[0012] In the known methods described above, the minimum feature sizesuiting the needed application (e.g., three-dimensional microscopicstructure) is determined through known simulation techniques, byexperimentation or other methods. Once the minimum feature size isdetermined, a pixel defining the mask dimensions is generated. Variousmethods have been applied to array a gray scale design (e.g., squares,pixels or spots using variable pitch and variable sub-pixelationmethods). These methods, however, have their limitations. In thisregard, it is known that contact hole and spot features are moredifficult to control than line and space features. As a result, bothcorner rounding and linearity of the design are compromised. Similarly,variable pitch methods are problematic since they require a differentalgorithm to be applied at each pixel position to carefully define thecorrect opening in the BHT mask. When considering the dynamic range forthe layout, the square pixel changes non-linearly since the size isvaried over the contact area. This can limit the ability of a maskdesigner to make the fine changes required to correct for processnon-linearity. These methods add to the costs and processing time inpreparation of the mask since they require a large number of adjustmentsto be made to the overall design.

[0013] One example of a known method for designing a BHT photomask isdescribed in U.S. Pat. No. 5,310,623 (“the ‘623 patent’). The '623patent teaches a method for fabricating microlenses through the use of asingle exposure mask with precisely located and sized light transmittingopenings to enable an image replica to be produced in photoresistmaterials, and ultimately transferred to a substrate. As disclosed, thedesign for the photomask is generated using three-dimensional modelingsoftware, wherein a single pixel defines the shape of the microlens. Thesingle pixel is sub-divided into “sub-pixels”, which in turn aresub-divided into gray scale resolution elements. Each sub-pixel and grayscale resolution elements is designed to be “equal [in] size” on eachside. (Col. 6, line 30). In other words, each sub-pixel and gray scaleelement is a perfect square.

[0014] U.S. Pat. No. 6,335,151 discloses a method for fabricating amicroscopic, three-dimensional object by creating a mask havingconsisting of pixels and “super-pixels” which define the contours of theobject's surface, imaging the mask's pattern onto a photoresist film,and transferring the three-dimensional surface from the photoresist to asubstrate.

[0015] Although useful, the conventional square pixel array methods usedin the prior art have their shortcomings. In this regard, the prior artdiscloses the use of square pixels having a size which is less than theminimum resolvable feature size of an optical system. Each pixel is thendivided into sub-pixels whose respective areas are changed in both the xand y axes, as disclosed in the '151 and '623 patents. As a result, thechange in area of each sub-pixel is a square of the amplitude, therebymaking the change in light intensity between each gray level non-linearand often infinite. Thus, the transmission of light is limited by thesquare sub-pixel's size as well as the minimum dimensions permitted bythe mask pattern generator. Accordingly, three-dimensional objects madeby the prior art methods tend to have jagged surfaces, especially wherethe objects are sloped. Since these methods produce marginal results,many have migrated away from the use of BHT photomasks for makingthree-dimensional microscopic devices.

[0016] Thus, there is a long felt need for new design rules and layoutchoices for making BHT photomasks to overcome these shortcomingassociated with the prior art.

[0017] While the prior art is of interest, the known methods andapparatus of the prior art present several limitations which the presentinvention seeks to overcome.

[0018] In particular, it is an object of the present invention toprovide a method for designing a BHT photomask layout having a smoothprofile.

[0019] It is a further object of the present invention to provide amethod for designing a BHT photomask layout which meets thespecifications of a wide range of optical systems.

[0020] It is another object of the present invention to design a BHTphotomask wherein the change in light intensity between each gray levelis both linear and finite.

[0021] It is another object of the present invention to solve theshortcomings of the prior art.

[0022] Other objects will become apparent from the foregoingdescription.

SUMMARY OF THE INVENTION

[0023] It has now been found that the above and related objects of thepresent invention are obtained in the form of a BHT photomask andmicroscopic three-dimensional structure and method for designing andfabricating the same. The method for designing the layout of BHT or grayscale photomasks is governed by specific design rules calculated withinan electronic database.

[0024] More particularly, the present invention is directed to a binaryhalf tone photomask comprising a substantially transparent substrate andan opaque layer having a pattern formed therein. The pattern is definedby at least one pixel, wherein each pixel is divided into sub-pixelshaving a variable length in a first axis and fixed length in a secondaxis. In one embodiment of the present invention, the pixel is a squareand the sub-pixels have a height and a length, wherein th height of eachof the sub-pixels is approximately one half of the pixel's pitch and thelength of each sub-pixel is linearly varied in opposite directions alongone axis only. In another embodiment, the pixel is circular and thesub-pixels have a radius and an arc length, wherein the radius of eachof the sub-pixels is approximately one half of the pixel's pitch and thearc length of each sub-pixel being linearly varied in oppositedirections along one axis only.

[0025] The present invention is also directed to a method for designinga layout of a binary half tone photomask pattern to be used to fabricatea three-dimensional structure. This method comprises the steps ofgenerating at least two pixels, dividing each of the pixels intosub-pixels having a variable length in a first axis and fixed length ina second axis, and arraying the pixels to form a pattern fortransmitting light through the pixels so as to form a continuous tone,aerial light image. In a preferred embodiment, the sub-pixel's area issmaller than the minimum resolution of an optical system of an exposuretool with which the binary half tone photomask is intended to be used.

[0026] Additionally, the present invention is directed to a method formaking a binary half tone photomask. This method comprises the step ofproviding a binary photomask comprising a photoresist layer, an opaquelayer and a substantially transparent layer in a lithography tool.Additionally, the photoresist layer is exposed to the lithography toolin accordance with a binary half tone photomask pattern on thephotomask, wherein the pattern is defined by at least one pixel. Eachpixel is divided into sub-pixels having a variable length in a firstaxis and fixed length in a second axis. Next, undesired portions of thephotoresist and portions of the opaque layer underlying the removedphotoresist portions are etched. Thereafter, the remaining portions ofthe photoresist layer are removed. Here again, each sub-pixel's area ispreferably smaller than the minimum resolution of an optical system ofan exposure tool with which the binary half tone photomask is intendedto be used.

[0027] The present invention is also directed a microscopicthree-dimensional structure made in accordance with the methodsdescribed above. In this regard, the three-dimensional structurecomprises a wafer having a continuous tone, substantially linear andsmooth surface, wherein the surface of the wafer corresponds to theshape of a light aerial image generated from a binary half tonephotomask. The binary half tone photomask comprises a pattern formedtherein which is defined by at least one pixel, wherein each pixel isdivided into sub-pixels having a variable length in a first axis andfixed length in a second axis. Here again, each sub-pixel preferably hasan area that is smaller than the minimum resolution of an optical systemof an exposure tool with which the binary half tone photomask isintended to be used.

[0028] The present invention is also directed to a method forfabricating a three-dimensional microscopic structure in accordance withthe methods described above. In this regard, the method for fabricatinga three dimensional structure comprises the step of providing a binaryhalf tone photomask between an exposure tool and a wafer coated with aphotoresist layer. The binary half tone photomask comprises asubstantially transparent substrate and an opaque layer having a patternformed therein. The pattern is defined by at least one pixel, whereineach pixel is divided into sub-pixels having a variable length in afirst axis and fixed length in a second axis. The sub-pixels' area ispreferably smaller than the minimum resolution of an optical system ofan exposure tool with which the binary half tone photomask is intendedto be used. Next, the photoresist layer of the wafer is exposed to theexposure tool in accordance with pattern on the binary half tonephotomask. Thereafter, undesired photoresist is removed to form athree-dimensional profile in the photoresist which has not been removed.Next, the wafer is etched to a predetermined depth to correspond inshape to the three dimensional profile formed in the remainingphotoresist. Thereafter, the remaining photoresist is removed.

[0029] In another embodiment of the present invention, a method formaking step and flash templates is provided. This method comprises thestep of providing a binary photomask having a photoresist layer, anopaque layer and substantially transparent in a lithography tool. Thephotoresist layer is exposed to a lithography tool in accordance with abinary half tone photomask pattern defined by at least one pixel,wherein each pixel is divided into sub-pixels having a variable lengthin a first axis and fixed length in a second axis. The sub-pixels' areais preferably smaller than the minimum resolution of an optical systemof an exposure tool with which the binary half tone photomask isintended to be used. Next, undesired portions of the photoresist isremoved from the photomask and portions of the chrome layer underlyingthe removed photoresist portions are etched away. Thereafter, remainingportions of the photoresist layer are removed and the pattern in thebinary half tone photomask is transferred to a second substrate toproduce a continuous tone pattern defined by the photomask thereon. Thesecond substrate is preferably made from a rigid material, including,but not limited to, fused silica, glass, metals, crystalline structures,plastics or other similar materials. The second substrate may then beused as an imprinting or stamping plate for fabricating imprintlithography applications.

[0030] Another embodiment of the present invention is directed to a grayscale photomask made in accordance with the methods described herein.The gray scale photomask comprises a substantially transparent substrateand an opaque layer having a pattern formed therein. The pattern isdefined by at least one pixel, wherein each pixel is divided intosub-pixels having a variable length in a first axis and fixed length ina second axis. The sub-pixels' area is preferably smaller than theminimum resolution of an optical system of an exposure tool with whichthe binary half tone photomask is intended to be used.

BRIEF DESCRIPTION OF THE DRAWINGS

[0031] The above and related objects, features and advantages of thepresent invention will be more fully understood by reference to thefollowing, detailed description of the preferred, albeit illustrative,embodiment of the present invention when taken in conjunction with theaccompanying figures, wherein:

[0032]FIGS. 1 and 2 illustrate examples of BHT photomask patterns knownin the prior art;

[0033]FIG. 3 illustrates the ripple effect that results from a step-ramplayout designed in accordance with prior art sub-pixelation methods,such as those shown in FIGS. 1 and 2;

[0034]FIG. 4 illustrates the process of making BHT photomask patternusing conventional lithography techniques;

[0035]FIGS. 5a and 5 b show a square pixel divided into half-pitchsub-pixels whose area is varied along one axis only in accordance withthe method of the present invention;

[0036]FIGS. 6a and 6 b show a circular pixel divided into half-pitchsub-pixels whose area is varied along one axis only in accordance withthe method of the present invention;

[0037]FIG. 7 shows the surface roughness of a three-dimensional deviceas it relates to photoresist thickness and the critical dimensions ofthe device;

[0038]FIG. 8 shows the dynamic range of BHT gray levels pixel sizes as afunction of photoresist contrast;

[0039]FIG. 9 shows a linear ramp design for a BHT photomask made inaccordance with the method of the present invention as shown in FIGS. 5aand 5 b;

[0040]FIG. 10 is an SEM cross section of a printed BHT design on awafer;

[0041]FIG. 11 shows an AFM profile of the photoresist slope of the rampdesign shown in FIGS. 9 and 10;

[0042]FIG. 12 shows a simulated photoresist profile from the design ofFIGS. 9 and 13;

[0043]FIG. 13 shows circular ramp design for BHT photomask made inaccordance with the method of the present invention as shown in FIGS. 6aand 6 b;

[0044]FIG. 14 is an AFM image of a lens array that was printed inaccordance with the ramp design shown in FIG. 13;

[0045]FIG. 15 shows a side view of one of the conical sections shown inFIG. 14; and

[0046]FIG. 16 is a pixel having multiple sub-pixels arrayed therein.

DETAILED DESCRIPTION OF THE INVENTION

[0047] The present invention generally relates to improved BHTphotomasks and microscopic three-dimensional structures made from suchphotomasks. The present invention is also directed toward a method fordesigning and fabricating BHT photomasks to be used in creating suchmicroscopic three-dimensional structures (e.g., MEMS, micro-optics,photonics, micro-structures and other three-dimensional, microscopicdevices). More particularly, the present provides a method for designinga BHT photomask layout, transferring the layout to a BHT photomask andfabricating three-dimensional microscopic structures using the BHTphotomask designed by the method of the present invention. As will beseen below, the method of the present invention enables a photomaskdesigner to design a BHT photomask to have continuous gray levels suchthat the change in light intensity between each gray level is bothfinite and linear. As a result, when this BHT photomask is used to makea three-dimensional microscopic structure, it is possible to produce asmoother and more linear profile on the object being made. Likewise, ithas been found that BHT photomasks designed in accordance with themethod of the present invention meet the sub-resolution requirements ofmost, if not all, optical tools. Each aspect of the present invention isnow described.

[0048] The first aspect of the present invention is directed to themethod by which the design for a BHT photomask is generated. Moreparticularly, the method of the present invention implements specificdesign rules calculated within an electronic database to generate aphotomask pattern which achieves substantially linear changes invariable light intensity when transmitted through the photomask.

[0049] More particularly, the BHT photomask design method of the presentinvention uses a series of pixels, preferably either square or circular,whose area is varied in a manner so as to avoid the limitations of theresolution of the mask pattern generator being used. (While square orcircular pixels are preferred, the present invention is not so limited,and may apply to other shaped pixels, such as oval shaped, rectangular,etc.). In a preferred embodiment, a pixel 19 is generated such that itsarea is larger than the minimum resolution of the mask pattern generatorbeing used. Thereafter, each pixel 19 is divided into two half-pixels,such as sub-pixels 21 a and 21 b, as shown in FIGS. 5a-b and 6 a-b. Eachsub-pixel 21 a and 21 b has a height h (in the case of a square pixel,see FIGS. 5a-b) or radius r (in the case of a circular pixel, see, FIGS.6a-b), wherein the height h or radius r for each sub-pixel 21 a and 21 bis a fixed length. In one embodiment, the height h or radius r of eachsub-pixel 21 a and 21 b, as the case may be, is equal to approximatelyone-half of the pitch p of pixel 19. It is noted, however, that theheight h or radius r (as the case may be) of the sub-pixels 21 a and 21b can be divided into other fixed lengths, including, but not limitedto, the following arrangements: height h or sub-pixel 21 a is one-thirdof the pitch of the pixel 19 and sub-pixel 21 b is two-thirds of thepitch of pixel 19, or vice versa; height h or sub-pixel 21 a isone-fourth of the pitch of the pixel 19 and sub-pixel 21 b isthree-fourths of the pitch of pixel 19, or vice versa; etc. In thisregard, the height h or radius r of each sub-pixel 21 a and 21 b shouldbe divided in a manner such that their total pitch, when added together,is equal to the pitch of the pixel 19 from which they were divided.Next, the length l (in the case of a square pixel) or arc θ (in the caseof a circular pixel) of each sub-pixel is varied in opposite directionsalong one axis only, in a staggered arrangement to either increase ordecrease the total area of the full pixel, depending upon the particularpattern design being generated, as shown in FIGS. 5a-b and 6 a-b,respectively. In this regard, the area of each sub-pixel 21 a and 21 bshould be linearly varied to an amount that is equal to or less than theminimum resolvable pitch of the optical system of the exposure toolbeing used. Additionally, where only a small number of sub-pixels arearrayed to form the BHT photomask design, it is preferable that thepixels 19 are sized to meet the minimum resolution of the exposure toolbeing used to ensure that the sub-pixels 21 a and 21 b will not beresolved during the image writing process, and thus, avoid thesub-ripple effects exhibited by the prior art. Each modified pixel 19 ishereinafter referred to as a Half-Pitch Expansion Cell (“HPEC”). Thisprocess is repeated, with a series of HPECs being arrayed in a manner toreflect the design of the three-dimensional device to be fabricated. Byarraying the HPECs in this manner, continuous gray levels are createdsuch that the change in light intensity between each gray level (i.e.,amplitude) is both linear and finite. In this regard, since the numberof possible gray levels in the patterned array is increased by thismethod, the BHT mask design achieves a substantially continuous,variable pixel size from the maximum opening to the smallest opening toyield 100% to 0% transmission through the mask. As a result, smoothersurfaces are created on the three-dimensional object being formed withthe BHT photomask.

[0050] The arrayed design is created as a hierarchical, two-dimensionalimage written within a Computer Aided Design (“CAD”) system. Any CADtool having all-angle polygon capability can be used to write the pixels19 for the purposes of the present invention. One example of anappropriate a mask pattern generator to write a pixel is the L-Edit CADtool by Tanner EA.

[0051] The hierarchical design created with the method of the presentinvention incorporates a layer for each gray level and allows each HPECto be arrayed uniquely from other gray levels. This hierarchical designis used to compile a mask pattern generator file for writing the BHTpattern on a photomask, with the hierarchy being maintained in suchfile. By using this method, the mask pattern generator file size remainsvery small compared to one that has been flattened where all gray levelpixels are within a single layer, as is the case using prior artmethods. As a result, it is possible to achieve a quicker write time,thereby reducing the cost to manufacture the photomask. Furthermore, ithas been found that BHT layouts designed by the method of the presentinvention are more easily arrayed with a repeating symmetry that lendswell to polar and orthogonal arrays without interference from onesub-pixel to another. In this regard, unlike the prior art, whichrequired a pattern to be rewritten each time it was transferred to awafer, the method of the present invention allows a pattern to betransferred in a serial manner once it is arrayed. This too results infaster processing time to manufacture the resulting devices, and thus,greater throughput.

[0052] Furthermore, by forming the HPECs in accordance with the methodof the present invention, the sub-pixels 21 a and 21 b should be belowthe minimum resolution of most optical systems of exposure tools. Thus,unlike the prior art, the BHT design made in accordance with the presentinvention is limited only by the CAD tool design grid that is chosen toarray the mask pattern (which is typically 1 nm, but may be other sizesif desired) and the CAD tool being used. Moreover, as should beunderstood from the foregoing, the sub-pixels 21 a and 21 b are createdas a single cell within a design having a width which can be modulatedfor each gray level, while at the same time maintaining a constant pitchfor that gray level. Thus, when each sub-pixel 21 a and 21 b is arrayedwith a layer and each gray level has an assigned layer, the single cellopen area can be easily changed for the photoresist process whencorrection for process non-linearity are required.

[0053] In the second, related aspect of the present invention, the maskpattern generator file is transferred to a photomask. In this regard, ablank photomask is made using a standard binary (e.g., chrome-on-quartz)photomask and conventional lithography techniques, as shown in FIG. 4.Preferably, the blank binary photomask is a standard chrome-on-quartzphotomask coated with a photoresist layer 51. It is noted however, thatthe photomask may have other layers (e.g., an anti-reflective layer suchas CrO) if needed or desired. To process the photomask, designatedportions of the photosensitive material on the photomask are exposed tothe mask pattern generator in accordance with the BHT photomask designstored in the mask pattern generator file and the exposed portions ofthe photoresist are removed such that the chrome portions 53 are nolonger covered by the photoresist 51. Next, the uncovered chromeportions 53 are etched away using standard techniques (e.g., wet or dryetching), thereby exposing the quartz portions 55 underlying the areasof removed chrome 53. Thereafter, the remaining photoresist (i.e., theunexposed photoresist) is removed. The result is a BHT photomask havingthe BHT design etched thereon. The opaque portions 53 of the BHTphotomask attenuates the passage of light energy through the mask suchthat the transmitted light will have varying intensity as governed bythe photomask design.

[0054] In the third, related aspect of the present invention, the designfor the three-dimensional microscopic structure is transferred from theBHT photomask to a wafer to form the desired three-dimensionalstructure. In this regard, the BHT photomask designed in accordance withthe method of the present invention is placed between a wafer exposuretool (e.g., stepper) or other lithographic camera and a wafer havingphotoresist (e.g. AZ 4400) deposited thereon. Light is then transmittedfrom the wafer exposure tool through the openings in the BHT photomaskin a uniform, substantially linear manner to produce a three-dimensionallight aerial image. The photoresist on the wafer is in turn exposed tothis three-dimensional aerial light image and developed to remove theexposed photoresist. As a result, a three-dimensional surfacecorresponding to the aerial image is formed in the photoresist. Next,the wafer is etched to a predetermined depth to correspond in shape tothe developed photoresist. As a result, a three-dimensional image,defined by the BHT photomask, is formed on the wafer.

[0055] To achieve optimal linear results in designing a BHT photomask inaccordance with the present invention, there are several design andprocessing considerations which a photomask designer should considerwhen designing a BHT photomask layout. In particular, the designershould consider the limitations of the CAD tool and write tool beingused as well as the limitations of the wafer device being used tofabricate the three-dimensional device. Each of these considerations arediscussed below. However, it is noted that there may be other designconsiderations (e.g., active device tolerances and system resolutionneeded to accurately reproduce the active device) depending upon the BHTprocess being used and the device being made which a photomask designermay consider.

[0056] As noted herein, a variety of different CAD tools may be used,provided that such CAD tools have all-angle capability. Thus, dependingupon the CAD tool being used, the size of design grid may vary.Likewise, depending upon the mask pattern generator being used, the sizeof the write grid may also vary. For example, at the present time,conventional mask write grid values are typically even multiples of thedesign grid, both of which generally range between 5 nm and 200 nm. Itshould be noted, however, that the design and write grid value can alsobe other values (e.g., 0.1 nm, 1.5 nm, etc), including for example,non-integers, fractions, etc. In such cases, the design grid and graylevel pixel size variation would need to be adjusted to fit the writetool grid in order to minimize the snap-to-grid that occurs when thedesign data is converted into the write tool grid format. Thus, thepresent invention is not limited to the write tools and write gridsdescribed herein, as these tools are merely described for exemplarypurposes. In a preferred embodiment, when a BHT photomask design ispatterned onto a photomask substrate, the design should be adjusted tofit the mask pattern generator write grid. In this regard, it ispreferred that the size of the write grid is equal to the size of thedesign grid. The number of gray levels that are possible in the designis governed by the equation (2) as follows:

#Gray Levels for BHT photomask design=D _(y) /W _(g)  (2)

[0057] where W_(g) is the writer grid value and D_(y) is the sub-pixelsize. Referring to Table 1 below, the difference in area change for awrite tool address, the possible number of gray levels for a design andthe pixels' critical dimensions size at the minimum energy thresholdE_(o) 10% of area is shown for both the HPECs designed in accordancewith the method of the present invention as well as a conventionalsquare pixel layout of the prior art. In this example, the pixel's sizein each case is 2.5 microns. TABLE 1 Variation of Pixel Area by SizingMaximum Number of Pixel CD at of 1 Address Unit Gray Levels E_(o) WriteTool Address, nm Write Tool Address, nm 10% of Area 5 25 100 200 5 25100 200 X Y Half- 0.20% 1.00% 4.00% 8.00% 400 80 20 10 500 1250 PitchSquare 0.80% 3.96% 15.36% 29.44% 200 40 10  5 791  791

[0058] As can be seen, when the HPEC is changed in only one axis, thechange in area is a linear function in multiples of the address unit.When the square pixel is changed in both axes, the change in area is anexponential function, with the address unit being the exponent. As aresult, there is a non-linear change using the square pixel method.Moreover, when the area of the HPEC is varied as described herein, thenumber of possible gray levels doubles for a given dynamic range ascompared with the square pixel method. Additionally, the light intensityis sufficiently low at the minimum energy threshold E_(o) such that thephotoresist will be unresolvable when exposed.

[0059] In addition to considering the number of gray levels that arepossible in a design, the mask designer should also consider whether itis possible to actually transfer these gray levels to the wafer devicefor which the BHT design is being designed. In this regard, the maskdesigner should determine the dynamic range (e.g., total number of graylevels of the image) that can actually be printed to the wafer device,which is governed by the equation (3) as follows:

#Gray Levels to be printed on wafer=X/G _(w)  (3)

[0060] where x is the length of device and G_(w) is the width of anindividual gray scale region. Since the design and write grid for CADand write tools are measured in nanometers, the sub-pixel to sub-pixelvariation and the number of gray levels possible is limited only by thewafer device length X and not by the grid size W_(g). For example, if amicro-mirror is required to be X microns in length and the height isalso X microns, the resulting mirror angle will be 45 degrees after theresist exposure using a properly designed BHT photomask in accordancewith the present invention.

[0061] A photomask designer should also consider the specifications forthe surfaces of the micro-optical device being made. In this regard,surface roughness is a critical element in the optical efficiency of anoptical component. Thus, if the number of gray levels in a photomaskdesign is insufficient across the area of the design, the lightintensity image will exhibit discrete steps that may be intolerable forthe application. This problem is particularly prevalent in applicationswhere thick photoresist is used and the device design includes rapidchanges within short areas, as illustrated in FIG. 7. Thus, thephotomask designer should consider the type of photoresist being used onthe wafer in formulating a BHT design. In this regard, each type ofphotoresist process exhibits a unique response to the aerial image of anoptical exposure tool. For example, various changes in the photoresist'sthickness, bake conditions, dyes and absorption coefficients can changethe photoresist contrast or the slope of the contour of the BHTphotomask.

[0062] Accordingly, under a preferred embodiment of the presentinvention, the mask designer should determine the dynamic range of thephotoresist process being used. The dynamic range of the photoresistprocess is the range of the size of sub-pixels 21 a and 21 b. Thedynamic range of the photoresist process should preferably vary from theminimum sub-pixel opening required to achieve the minimum energythreshold E_(o) in the photoresist to the largest sub-opening requiredto achieve the maximum energy threshold E_(f) (i.e. dose-to-clear) inthe photoresist. It is within the dynamic range E_(o)-E_(f) that thegray scale variations should be applied.

[0063] In many cases, these responses with the dynamic range E_(o)-E_(f)will not be realized until after the BHT photomask is used and acalibrated response is observed with a particular design. Thus, it maybe necessary, depending upon the BHT photomask design and the experienceof the photomask designer, to fabricate a test BHT photomask and measureits response. Thereafter, a control design can be used to normalize thephotoresist to a linear response, where the pixel size variation iscalculated to be an equal change in transmitted light intensitythroughout the gray levels. This process may require one or moreiterations, depending upon the initial linearity achieved through thedesign. It should be noted, however, that as the mask designer becomesmore experienced with this method and learns how certain photoresistmaterials react in response to certain designs, it may not be necessaryto normalize the control design as more accurate results can be achievedfrom the initial design. Where measured and calibrated responses arerequired to fine tune the BHT photomask design, the mask designer shouldconsider that the amplitude of transmitted light through asub-resolution opening (e.g., sub-pixels 21 a and 21 b) is proportionalto the area of the opening. Accordingly, since the light intensitytransmitted through the opening is proportional to the magnitude squaredof the amplitude (i.e., I∝|A|²), then a linear change in wafer planeintensity is calculated by equation (4) as follows:

|A|∝I^(1/2)  (4)

[0064] where A is the amplitude of the light at the mask plane and I isthe intensity of the light at the wafer plane. Thus, when the sub-pixelis changed in one axis, there will be a linear change in intensity. Itis noted that further calibration may be needed in cases where it isnecessary to align three-dimensional features with two dimensionalfeatures in the same photomask. After photoresist calibration iscompleted, the variance from an expected response is measured. Thesevalues are then used to change the BHT photomask design, where eachsub-pixel's size in each of the gray levels of the design is eitherenlarged or reduced in area in one axis only, in accordance with thedisclosed method, to create the desired resist profile. As shown in FIG.8, as the photoresist contrast decreases, the dynamic range of thephotoresist process becomes wider. That is, the dynamic rangeE_(o)-E_(f) of the photoresist process changes with changes in thephotoresist contrast C as well as changes in the minimum resolution ofthe optical system being used. Thus, the wider the dynamic range, thegreater the number of gray levels possible within a BHT design.

[0065] Additionally, the photomask maker should consider the type ofoptical system in the exposure tool that will be used to make thethree-dimensional device. In this regard, it is preferable to use anoptical system that has a high reduction ratio so as to enable the maskmaker to print sub-pixels throughout the dynamic range and within thelatitude of the photomask making process. Additionally, as the pixelsize of the design decreases, write tools and processes having higherresolutions may be required, which can drive up the cost of the process.Thus, to avoid this problem, it is preferable to use a photoresistprocess having as large a dynamic range as possible, a relatively lowcontrast photoresist (e.g., AZ-4400 photoresist can be used to producemirrors and lenses in single mode clad/core/clad polymer waveguides) andan optical system having a relatively low numerical aperture and highmagnification. If, by contrast, the wafer has requirements to patternvery small structures, then a higher NA and/or lower process resolutionvariation K1 should be used, and the BHT photomask design should bemodified to perform under these conditions. Additionally, if necessary,the wafer designer can use multiple mask levels and double exposuretechniques at different NAs to achieve the optimum results.

[0066] AZ-4400 photoresist has been shown to exhibit desirabletransparency and photosensitivity at 365 nm. Referring to Table 2,typical flow for a process using the AZ-4400 resist is shown: TABLE 2Spin coat Softbake Expose PEB Develop Rinse Spin dry Temp RT 90 C. 240mj 110 C. 20 C. Gently RT Time As required 60 sec  60 sec  3 min Asrequired Speed As required Bath As required Chemistry AZ-4400 AZ-300 MIFDiH20

[0067] It is noted that care should be exercised in developing aphotoresist coating process so as to avoid a sunburst striation pattern,which typically occurs in thick photoresist coatings. Further, the smallthickness variations present in photoresist striations will bereproduced in the three-dimensional structures. Furthermore, the processcontrast can be reduced by under-baking the photoresist. It was foundthat a post-exposure bake worked well to diffuse the photoresistdevelopment inhibiter, minimizing the patterning of the binary halftonestep transitions.

[0068] Having described the overall method for designing and fabricatinga BHT photomask and design considerations regarding the same, specificexamples of the application of the method of the present invention arenow described.

[0069] Referring to FIG. 9, one embodiment of a BHT photomask designmade in accordance with the method of the present invention is shown.More particularly, the gray levels in the design of FIG. 9 provide aramp layout for a 45 degree micro-mirror, arrayed waveguide. When usingthe BHT photomask design of FIG. 9 and HPEC design method shown in FIGS.5a and 5 b with a 365 nm optical tool having an NA of 0.4 and a sigma of0.7, the BHT photomask transmitted light through its openings in acontinuous, linear fashion. Accordingly, photoresist on the wafer, whenexposed, resulted in a substantially smooth and linear profile, as shownin the SEM of FIG. 10. The wafer was then etched to a predetermineddepth to correspond to this resist profile. As shown in FIG. 11, a rampof 45 degree±2 degrees (the actual measure angle was approximately 46.5degrees) was printed on the wafer for this particular photonicsapplication. Additionally, the resulting surface on the wafer wassufficiently smooth for this particular photonic applications, as thesurface roughness was less than 20 nm, as shown in FIG. 11. Furthermore,in this embodiment, the mean slope (46 degrees) curvature and notchingwere accurately predicted through simulations of the BHT photomaskdesign, as shown in FIG. 12. More particularly, as shown in FIG. 12, thesimulations for this embodiment predicted the following: an angle of89.74 degrees for the profile of this design between lines 71 and 73 awhere the horizontal and vertical changes in the profile were 166 nm and7.214 Å, respectively; an angle of 46.5 degrees for the profile of thisdesign between lines 73 a and 73 b where the horizontal and verticalchanges were 3.689 μm and 3.501 μm, respectively; and an angle of 88.52degrees for the profile of this design between lines 75 a and 75 b wherethe horizontal and vertical changes were 196 nm and 5.050 nm,respectively.

[0070]FIG. 13 shows another embodiment of a BHT mask design made fromthe polar coordinate array made in accordance with the method of thepresent invention. This mask design could be used, for example, tofabricate micro-optical components, such as a micro-lens or a conicalsection. In this embodiment, a lens was printed using the circular BHTphotomask design of FIG. 13 and the HPEC design methods of the presentinvention as shown in FIGS. 6a and 6 b. This particular BHT photomaskwas used with a 365 nm optical tool having an NA of 0.4 and a sigma of0.7. A substantially smooth and linear photoresist profile was formedusing this design, as shown in the AFM images of FIGS. 14 and 15. As canbe seen, conical section objects were produced and exhibited nosub-ripple effect in the device.

[0071] In another embodiment, the HPEC method of the present inventionwas used to print a specific sloped structure for a photonicapplication. In this embodiment, an Applied Materials ALTA 3500 laserwriter was used on a 5 nm write grid. The ALTA 3500 laser writer was thebest choice for this embodiment because it had a pixel-to-pixel criticaldimension linearity at the wafer dimension which was similar to thewrite tool grid size. It is noted, however, that in other applications,more advanced e-beam and laser mask pattern generators (e.g., a CORE2564, MEBES 4500 E-beam tool, etc.) having smaller grid sizes (e.g., 1.5nm-2.5 nm) may also be used provided that the BHT photomask design canbe fitted to the write tool grid and the desired gray levels can beachieved. Additionally, in this embodiment, a dry plasma chrome etch wasused to process the BHT photomask. It is noted, however, wet etchtechniques may be alternatively used. In such cases, response fidelityand gray scale performance will be limited by the write tool grid, andcompromised by the mask bias. Irrespective of which etching techniqueand mask write tool is used, the linearity in the critical dimensions ofthe design must be maintained. Thus, to the extent the design exhibitsnon-linearity, such design should be corrected after the calibration ofthe wafer process is completed and compensated for in the BHT design. Byusing this type of process, mask dimensions can be controlled in alinear fashion for small sub-pixel sizes ranging from 0.4 μm to the fullpixel size of 2.5 μm when the ALTA 3500 write tool is used.

[0072] In another embodiment, the HPEC method of the present inventionis used to develop step and flash templates. In this regard, a BHTphotomask is made in accordance with the HPEC design method of thepresent invention. Thereafter, the three-dimensional image defined bythe photomask is transferred in a reduction lithography system to asecond substrate to produce a second photomask with continuous tone(i.e., gray scale) patterns. This second mask serves as an imprinting orstamping template for imprint lithography applications. The secondphotomask should preferably be made from a rigid material capable ofoperating as a stamp. For example, the second photomask may be made froma variety of different rigid materials, including, but not limited to,fused silica, glass, metals, crystalline structures, plastics and anyother rigid material now known or hereinafter developed. In thisembodiment, the second photomask is used to stamp or mold athree-dimensional structure. This may be done using an imprint steppersuch as a Molecular Imprints stepper or other known or hereinafterdeveloped tools.

[0073] Now that the preferred embodiments of the present invention havebeen shown and described in detail, various modifications andimprovements thereon will become readily apparent to those skilled inthe art. For example, in addition to designing BHT photomasks, the HPECmethod of the present invention could be modified to design gray scalephotomasks (e.g., 0%, 50%, 100%, etc. transmissivity) to be used to makethree-dimensional microscopic structures. Additionally, it is noted thateach pixel can be divided into thirds, quarters, fifths, etc. to formthree, four, five, etc. sub-pixels, respectively. In such cases, thearea of each sub-pixel should be varied along one axis only inaccordance with the methods described herein. For example, as shown inFIG. 16, a pixel 19 can be sub-divided in 4 sub-pixels 21 a, 21 b, 21 cand 21 d. In this example, each sub-pixel 21 a-d is sub-divided to beone half of the pitch of the pixel 19 in a first axis with the width ofeach sub-pixel 21 a-d being varied along a second axis. Moreover, it isnoted that the HPECs designed in accordance with the method of thepresent invention could be combined on a photomask with other devicedesigns (e.g., two dimensional binary structures such as an integratedcircuit). The present embodiments are therefor to be considered in allrespects as illustrative and not restrictive, the scope of the inventionbeing indicated by the appended claims, and all changes that come withinthe meaning and range of equivalency of the claims are thereforeintended to be embraced therein.

What is claimed is:
 1. A binary half tone photomask comprising: asubstantially transparent substrate; an opaque layer having a patternformed therein, said pattern defined by at least one pixel, wherein eachpixel is divided into sub-pixels having a variable length in a firstaxis and fixed length in a second axis.
 2. The binary half tonephotomask of claim 1, wherein said sub-pixels' area is smaller than theminimum resolution of an optical system of an exposure tool with whichsaid binary half tone photomask is intended to be used.
 3. The binaryhalf tone photomask of claim 1, wherein said pixel is a square.
 4. Thebinary half tone photomask of claim 3, wherein said sub-pixels have aheight and a length, said height of each of said sub-pixels beingapproximately one-half of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 5. The binary half tone photomask of claim 3, wherein saidsub-pixels have a height and a length, said height of each of saidsub-pixels being approximately one-third, one-fourth or one-fifth ofsaid pixel's pitch and said length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 6. The binary halftone photomask of claim 4, wherein said pixels are arrayed to form aramp layout for a photonic application.
 7. The binary half tonephotomask of claim 1, wherein said pixel is circular.
 8. The binary halftone photomask of claim 7, wherein said sub-pixels have a radius and anarc length, said radius of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said arc length of each sub-pixelbeing linearly varied in opposite directions along one axis only.
 9. Thebinary half tone photomask of claim 7, wherein said sub-pixels have aradius and an arc length, said radius of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 10. The binary half tone photomask ofclaim 1, wherein said pixel is oval-shaped.
 11. The binary half tonephotomask of claim 10, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said arc length of each sub-pixelbeing linearly varied in opposite directions along one axis only. 12.The binary half tone photomask of claim 10, wherein said sub-pixels havea radius and an arc length, said radius of each of said sub-pixels beingapproximately one third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 13. The binary half tone photomask ofclaim 1, wherein said at least one pixel is rectangular.
 14. The binaryhalf tone photomask of claim 13, wherein said sub-pixels have a heightand a length, said height of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said length of each sub-pixel beinglinearly varied in opposite directions along one axis only.
 15. Thebinary half tone photomask of claim 13, wherein said sub-pixels have aradius and an arc length, said radius of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 16. The binary half tone photomask ofclaim 1, wherein said opaque layer is chrome and said substantiallytransparent layer is quartz.
 17. The binary half tone photomask of claim1, further comprising a binary, resolved pattern in said opaque andsubstantially transparent layers.
 18. The binary half tone photomaks ofclaim 17, wherein said binary, resolved pattern defines the shape of atwo-dimensional integrated circuit design.
 19. A method for designing alayout for a binary half tone photomask pattern to be used to fabricatea three-dimensional structure comprising the steps of: generating atleast two pixels; dividing each of said at least two pixels intosub-pixels having a variable length in a first axis and fixed length ina second axis; and arraying said at least two pixels to form a patternfor transmitting light through said at least two pixels so as to form acontinuous tone, aerial light image.
 20. The method of claim 19, whereinsaid sub-pixel's area is smaller than the minimum resolution of anoptical system of an exposure tool with which said binary half tonephotomask is intended to be used.
 21. The method of claim 19, whereinsaid at least one of said pixels is a square.
 22. The method of claim21, wherein said sub-pixels have a height and a length, said height ofeach of said sub-pixels being approximately one-half of said pixel'spitch and said length of each sub-pixel being linearly varied inopposite directions along one axis only.
 23. The method of claim 21,wherein said sub-pixels have a height and a length, said height of eachof said sub-pixels being approximately one-third, one-fourth orone-fifth of said pixel's pitch and said length of each sub-pixel beinglinearly varied in opposite directions along one axis only.
 24. Themethod of claim 19, wherein at least one of said pixels is circular. 25.The method of claim 24, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said arc length of each sub-pixelbeing linearly varied in opposite directions along one axis only. 26.The method of claim 24, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-third, one-fourth or one-fifth of said pixel's pitch and said arclength of each sub-pixel being linearly varied in opposite directionsalong one axis only.
 27. The method of claim 19, wherein said at leastone is said pixels is oval-shaped.
 28. The method of claim 27, whereinsaid sub-pixels have a radius and an arc length, said radius of each ofsaid sub-pixels being approximately one-half of said pixel's pitch andsaid arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 29. The method of claim 27, wherein saidsub-pixels have a radius and an arc length, said radius of each of saidsub-pixels being approximately one-third, one-fourth or one-fifth ofsaid pixel's pitch and said arc length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 30. The method ofclaim 19, wherein said at least one of said pixels is rectangular. 31.The method of claim 30, wherein said sub-pixels have a height and alength, said height of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said length of each sub-pixel beinglinearly varied in opposite directions along one axis only.
 32. Themethod of claim 30, wherein said sub-pixels have a height and a length,said height of each of said sub-pixels being approximately one-third,one-fourth or one-fifth of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 33. The method of claim 19, further comprising the step of using amask pattern generator to write said at least one pixel and sub-pixels.34. The method of claim 33, wherein said mask pattern is generated froma computer aided design system having all angle capability.
 35. Themethod of claim 33, wherein said step of arraying further comprises thestep of incorporating a layer in said design for each gray level. 36.The method of claim 32, further comprising the step of compiling a maskpattern generator file.
 37. The method of claim 36, wherein saiddesign's hierarchy of gray levels is maintained in said file.
 38. Themethod of claim 37, further comprising the step of determining themaximum number of gray levels that can be written for said binary halftone photomask design.
 39. The method of claim 38, wherein said maximumnumber of gray levels is calculated by dividing said mask generator'swriter grid value by said sub-pixels' size.
 40. The method of claim 19,further comprising the step of determining the possible number of graylevels that can be printed on a wafer device using said binary half tonephotomask design.
 41. The method of claim 40, wherein said possiblenumber of gray levels is calculated by dividing said wafer's devicelength by an individual gray scale region's width.
 42. The method ofclaim 19, further comprising the step of determining a dynamic range fora photoresist process to be used in making a three dimensional deviceusing said binary half tone photomask design.
 43. The method of claim42, wherein said dynamic range varies from said sub-pixels' minimumopening size to said sub-pixels' maximum opening size.
 44. The method ofclaim 42, further comprising the step of applying gray scale variationsto said design within said dynamic range.
 45. The method of claim 42,further comprising the step of generating a test photomask in accordancewith said design.
 46. The method of claim 45, further comprising thestep of observing said test photomask's dynamic range by exposing awafer having photoresist thereon to an exposure tool.
 47. The method ofclaim 46, further comprising the step of normalizing said photoresist'sresponse to said test mask to achieve a linear response in transmissionof light through the photomask.
 48. The method of claim 47, furthercomprising the step of calculating said pixel's size variation to be anequal change in transmitted light intensity throughout each gray levelfor said design.
 49. The method of claim 47, wherein said linearresponse is achieved when the amplitude of light is proportional to thesquare root of said light's intensity.
 50. The method of claim 48,further comprising the step of comparing said photoresist's response toan expected result.
 51. A method for making a binary half tone photomaskcomprising the steps of: providing a binary photomask comprising aphotoresist layer, an opaque layer and a substantially transparent layerin a lithography tool; exposing the photoresist layer to saidlithography tool in accordance with a binary half tone photomask patternon said photomask, wherein said pattern is defined by at least onepixel, wherein each of said at least one pixel is divided intosub-pixels having a variable length in a first axis and fixed length ina second axis; removing undesired portions of said photoresist; etchingportions of said opaque layer underlying said removed photoresistportions; and removing remaining portions of the photoresist layer. 52.The method of claim 51, wherein said sub-pixel's area is smaller thanthe minimum resolution of an optical system of an exposure tool withwhich said binary half tone photomask is intended to be used.
 53. Themethod of claim 51, wherein said at least one pixel is a square.
 54. Themethod of claim 53, wherein said sub-pixels have a height and a length,said height of each of said sub-pixels being approximately one-half ofsaid pixel's pitch and said length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 55. The method ofclaim 53, wherein said sub-pixels have a height and a length, saidheight of each of said sub-pixels being approximately one-third,one-fourth or one-fifth of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 56. The method of claim 51, wherein said pixel is circular. 57.The method of claim 56, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-half of said pixel's pitch and said arc length of each sub-pixelbeing linearly varied in opposite directions along one axis only. 58.The method of claim 56, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-third, one-fourth or one-fifth of said pixel's pitch and said arclength of each sub-pixel being linearly varied in opposite directionsalong one axis only.
 59. The method of claim 51, wherein said step ofetching is performed by plasma dry etching techniques.
 60. The method ofclaim 51, wherein said step of etching is performed by wet etchingtechniques.
 61. A microscopic three-dimensional structure comprising: awafer having a continuous tone, substantially linear and smooth surface,said surface of said wafer corresponding to the shape of a light aerialimage generated from a binary half tone photomask, said photomaskcomprising a pattern formed therein, said pattern defined by at leastone pixel, wherein each pixel is divided into sub-pixels having avariable length in a first axis and fixed length in a second axis. 62.The microscopic three-dimensional structure of claim 61, wherein saidsub-pixels' area is smaller than the minimum resolution of an opticalsystem of an exposure tool with which said binary half tone photomask isintended to be used.
 63. The microscopic three-dimensional structure ofclaim 61, wherein said at least one pixel is a square.
 64. Themicroscopic three-dimensional structure of claim 63, wherein saidsub-pixels have a height and a length, said height of each of saidsub-pixels being approximately one-half of said pixel's pitch and saidlength of each sub-pixel being linearly varied in opposite directionsalong one axis only.
 65. The microscopic three-dimensional structure ofclaim 63, wherein said sub-pixels have a height and a length, saidheight of each of said sub-pixels being approximately one-third,one-fourth or one-fifth of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 66. The microscopic three dimensional device of claim 63, whereinsaid square pixels are arrayed to form a layout for a photonicapplication.
 67. The microscopic three-dimensional structure 64, whereinsaid layout is a ramp layout.
 68. The microscopic three-dimensionalstructure of claim 64, wherein an exposure tool that transmits light at365 nm, has an NA of 0.4 and sigma of 0.7 is used.
 69. The microscopicthree-dimensional structure of claim 61, wherein said pixel is circular.70. The microscopic three-dimensional structure of claim 69, whereinsaid sub-pixels have a radius and an arc length, said radius of each ofsaid sub-pixels being approximately one-half of said pixel's pitch andsaid arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 71. The microscopic three-dimensionalstructure of claim 69, wherein said sub-pixels have a radius and an arclength, said radius of each of said sub-pixels being approximatelyone-third, one-fourth or one-fifth of said pixel's pitch and said arclength of each sub-pixel being linearly varied in opposite directionsalong one axis only.
 72. The microscopic three-dimensional structure ofclaim 70, wherein said circular pixels are arrayed to form a conicalramp layout.
 73. The microscopic three-dimensional structure of claim70, wherein an exposure tool transmits light at 365 nm, has an NA of 0.4and a sigma of 0.7 is used.
 74. A method for fabricating athree-dimensional microscopic structure comprising the steps of:providing a binary half tone photomask between an exposure tool and awafer coated with a photoresist layer, said binary half tone photomaskcomprising a substantially transparent substrate, an opaque layer havinga pattern formed therein, said pattern defined by at least one pixel,wherein each pixel is divided into sub-pixels having a variable lengthin a first axis and fixed length in a second axis; and exposing thephotoresist layer of said wafer to the exposure tool in accordance withpattern on the binary half tone photomask.
 75. The method of claim 74,further comprising the step of removing undesired photoresist to form athree-dimensional profile in the photoresist which has not been removed.76. The method of claim 75, further comprising the step of etching saidwafer to a predetermined depth to correspond in shape to the threedimensional profile formed in said remaining photoresist.
 77. The methodclaim 74, wherein said sub-pixels' area is smaller than the minimumresolution of an optical system of an exposure tool with which saidbinary half tone photomask is intended to be used.
 78. The method claim74, wherein said pixel is a square.
 79. The method claim 78, whereinsaid sub-pixels have a height and a length, said height of each of saidsub-pixels being approximately one-half of said pixel's pitch and saidlength of each sub-pixel being linearly varied in opposite directionsalong one axis only.
 80. The method claim 79, wherein said sub-pixelshave a height and a length, said height of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 81. The method claim 74, wherein saidpixel is circular.
 82. The method claim 81, wherein said sub-pixels havea radius and an arc length, said radius of each of said sub-pixels beingapproximately one-half of said pixel's pitch and said arc length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 83. The method claim 81, wherein said sub-pixels have a radius andan arc length, said radius of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 84. A method for making step and flashtemplates comprising the steps of: providing a binary photomask having aphotoresist layer, an opaque layer and substantially transparent in alithography tool; exposing the photoresist layer to a lithography toolin accordance with a binary half tone photomask pattern, wherein saidpattern is defined by at least one pixel, wherein each pixel is dividedinto sub-pixels having a variable length in a first axis and fixedlength in a second axis; removing undesired portions of saidphotoresist; etching portions of said chrome layer underlying saidremoved photoresist portions; removing undesired portions of thephotoresist layer; transferring the pattern in said binary half tonephotomask to a second substrate to produce a continuous tone patterndefined by the photomask thereon.
 85. The method of claim 84, whereinsaid step of transferring is performed using a reduction lithographysystem.
 86. The method of claim 84, wherein said second substrate ismade from a rigid material.
 87. The method of claim 85, wherein saidsecond substrate is made from the group consisting of fused silica,glass, metals, crystalline structures and plastics.
 88. The method ofclaim 84, further comprising the step of using said second substrate asan imprinting or stamping plate for fabricating imprint lithographyapplications.
 89. A binary half tone photomask design layout comprising:at least two pixels, wherein each of said pixels is further defined bysub-pixels having a variable length in a first axis and fixed length ina second axis; a pattern formed by an array of said at least two pixelsfor transmitting light through said photomask so as to form a continuoustone, aerial light image.
 90. The binary half tone photomask designlayout of claim 89, wherein said sub-pixel's area is smaller than theminimum resolution of an optical system of an exposure tool with whichsaid binary half tone photomask is intended to be used.
 91. The binaryhalf tone photomask design layout of claim 89, wherein said at least oneof said pixels is a square.
 92. The binary half tone photomask designlayout of claim 91, wherein said sub-pixels have a height and a length,said height of each of said sub-pixels being approximately one-half ofsaid pixel's pitch and said length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 93. The binary halftone photomask design layout of claim 91, wherein said sub-pixels have aheight and a length, said height of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 94. The binary half tone photomaskdesign layout of claim 89, wherein at least one of said pixels iscircular.
 95. The binary half tone photomask design layout of claim 94,wherein said sub-pixels have a radius and an arc length, said radius ofeach of said sub-pixels being approximately one-half of said pixel'spitch and said arc length of each sub-pixel being linearly varied inopposite directions along one axis only.
 96. The binary half tonephotomask design layout of claim 94, wherein said sub-pixels have aradius and an arc length, said radius of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 97. The binary half tone photomaskdesign layout of claim 89, wherein at least one of said pixels isoval-shaped.
 98. The binary half tone photomask design layout of claim97, wherein said sub-pixels have a radius and an arc length, said radiusof each of said sub-pixels being approximately one-half of said pixel'spitch and said arc length of each sub-pixel being linearly varied inopposite directions along one axis only.
 99. The binary half tonephotomask design layout of claim 97, wherein said sub-pixels have aradius and an arc length, said radius of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said arc length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 100. The binary half tone photomaskdesign layout of claim 89, wherein said at least one of said pixels isrectangular.
 101. The binary half tone photomask design layout of claim100, wherein said sub-pixels have a height and a length, said height ofeach of said sub-pixels being approximately one-half of said pixel'spitch and said length of each sub-pixel being linearly varied inopposite directions along one axis only.
 102. The binary half tonephotomask design layout of claim 100, wherein said sub-pixels have aheight and a length, said height of each of said sub-pixels beingapproximately one-third, one-fourth or one-fifth of said pixel's pitchand said length of each sub-pixel being linearly varied in oppositedirections along one axis only.
 103. A gray scale photomask comprising:a substantially transparent substrate; an opaque layer having a patternformed therein, said pattern defined by at least one pixel, wherein eachpixel is divided into sub-pixels having a variable length in a firstaxis and fixed length in a second axis.
 104. The gray scale photomask ofclaim 103, wherein said sub-pixels' area is smaller than the minimumresolution of an optical system of an exposure tool with which said grayscale photomask is intended to be used.
 105. The gray scale photomask ofclaim 103, wherein said pixel is a square.
 106. The gray scale photomaskof claim 105, wherein said sub-pixels have a height and a length, saidheight of each of said sub-pixels being approximately one-half of saidpixel's pitch and said length of each sub-pixel being linearly varied inopposite directions along one axis only.
 107. The gray scale photomaskof claim 105, wherein said sub-pixels have a height and a length, saidheight of each of said sub-pixels being approximately one-third,one-fourth or one-fifth of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 108. The gray scale photomask of claim 105, wherein said pixelsare arrayed to form a ramp layout for a photonic application.
 109. Thegray scale photomask of claim 103, wherein said pixel is circular. 110.The gray scale photomask of claim 109, wherein said sub-pixels have aradius and an arc length, said radius of each of said sub-pixels beingapproximately one-half of said pixel's pitch and said arc length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 111. The gray scale photomask of claim 109, wherein saidsub-pixels have a radius and an arc length, said radius of each of saidsub-pixels being approximately one-third, one-fourth or one-fifth ofsaid pixel's pitch and said arc length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 112. The gray scalephotomask of claim 103, wherein said pixel is oval-shaped.
 113. The grayscale photomask of claim 112, wherein said sub-pixels have a radius andan arc length, said radius of each of said sub-pixels beingapproximately one-half of said pixel's pitch and said arc length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 114. The gray scale photomask of claim 112, wherein saidsub-pixels have a radius and an arc length, said radius of each of saidsub-pixels being approximately one-third, one-fourth or one-fifth ofsaid pixel's pitch and said arc length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 115. The gray scalephotomask of claim 103, wherein said at least one pixel is rectangular.116. The gray scale photomask of claim 115, wherein said sub-pixels havea height and a length, said height of each of said sub-pixels beingapproximately one-half of said pixel's pitch and said length of eachsub-pixel being linearly varied in opposite directions along one axisonly.
 117. The gray scale photomask of claim 115, wherein saidsub-pixels have a height and a length, said height of each of saidsub-pixels being approximately one-third, one-fourth or one-fifth ofsaid pixel's pitch and said length of each sub-pixel being linearlyvaried in opposite directions along one axis only.
 118. The gray scalephotomask of claim 103, wherein said opaque layer is chrome and saidsubstantially transparent layer is quartz.
 119. The gray scale photomaskof claim 103 further comprising a binary, resolved pattern in saidopaque and substantially transparent layers.
 120. The gray scalephotomaks of claim 119, wherein said binary, resolved pattern definesthe shape of a two-dimensional integrated circuit design.